Exact Results for Non-Newtonian Transport Properties in Sheared Granular Suspensions: Inelastic Maxwell Models and...

Area of Science:

• Physics
• Materials Science
• Fluid Dynamics

Background:

• Granular suspensions exhibit complex non-Newtonian behavior under shear flow.
• Previous models often used coarse-grained descriptions, neglecting real inter-particle collisions.
• Understanding these properties is crucial for various industrial applications.

Purpose of the Study:

• To determine the non-Newtonian transport properties of dilute granular suspensions under simple shear flow (USF).
• To account for real collisions between granular particles and a surrounding molecular gas.
• To derive exact expressions for rheological properties using two complementary kinetic theory approaches.

Main Methods:

• Utilized the Boltzmann kinetic equation for inelastic Maxwell models (IMM) to exploit velocity-independent collision rates for exact calculations.
• Employed a Bhatnagar-Gross-Krook (BGK)-type kinetic model adapted for granular suspensions to compute velocity moments and distribution functions.
• Compared theoretical results with approximate analytical methods (Grad's moment method) and computer simulations in the Brownian limit.

Main Results:

• Derived exact expressions for rheological properties in terms of key parameters like coefficient of restitution and mass ratio.
• Demonstrated good agreement between theoretical predictions and existing approximate methods/simulations.
• Observed an S-shaped curve for temperature and non-Newtonian viscosity, indicating discontinuous shear thickening (DST).

Conclusions:

• The study provides exact theoretical results for the rheology of sheared granular suspensions.
• Discontinuous shear thickening (DST) is confirmed as a key emergent property, becoming more pronounced with increasing mass ratio.
• The developed kinetic models offer a robust framework for analyzing granular material behavior.